Question

AJUTOOOORRR!!!! asimptota oblica spre + infinit la Gf. f(x)=x+1+1/x-1
2. F(X)>_4, apartine (1:+ infinit)

Answer 1

1.

y = mx+n

m = lim(x->+∞) f(x)/x = lim(x->+∞) ((x+1)/x + 1/(x*(x-1))) = 1

n = lim(x->+∞) (f(x)-mx) = lim(x->+∞) (1+1/(x-1)) = 1

Ecuatia asimptotei oblice spre +∞ este y = x+1

2.

f(x) = x-1 + 1/(x-1) + 2 ≥ 2+2 = 4 ⇒ f(x) ≥ 4, ∀x ∈ (1, +∞)

Am folosit faptul ca a+1/a ≥ 2, pt. orice a nr. real pozitiv (aici avem a = x-1)